Are you overclocking?
3770 is the best of those 3 CPU's, however for you the FX83 will probably be the best choice out of those 3.
Alternatively, there's an i7 Ivybridge Xeon at 170ish if you're not OC'ing that may also be an option.

I'd personally opt for the SB-E 3820. It's on the X79 platform, what still has an upgrade path to IB-E in the not too distant future, whereas the 3770k is now on a very probably dead platform (Haswell is on a new socket)

The 3820 and 3770k are near as makes no difference identical, both 4core 8threaded chips, both clock reasonable well (IB limited due to poor TIM under IHS) (SB-E due to no unlocked multi)

If money is really tight then going for AMD wouldn't be a bad choice...but not one most would recommend.

I don't think the 3770 is worth the extra over an i5 or an FX83.
The xeon I referred to is on Socket 1155, if you're not OC'ing then it could be the better chip for you, but then it really does come down to software as to how it performs against an FX83, neither would disappoint you for your usage.
It's called Intel Xeon E3-1230 V2

OP, Get the 8350 and get loads of RAM and other goodies with the money saved. It'll handle the tasks you require perfectly well. It won't get beaten by the 3770 and though will be passed by the 3820, not by much...and it will cost several hundred pounds left. As you won't be using it for gaming there is no reason at all to favour Intel.

OP, Get the 8350 and get loads of RAM and other goodies with the money saved. It'll handle the tasks you require perfectly well. It won't get beaten by the 3770 and though will be passed by the 3820, not by much...and it will cost several hundred pounds left. As you won't be using it for gaming there is no reason at all to favour Intel.

Well there's a post full of inaccuracies.

FYI, the 3770 > 3820.
The Ivybridge Xeon i7 is 20 quid more than the FX8350.

He'll save 20 quid going for the FX8350, not hundreds in the slightest.
He'd save 90 over the i7 3770.
He'd save about 130 over the 3820.

Out of those 3, as said, I'd take the FX8350, but I'm not going to lie about the hundreds of pounds saving.

The 3820 and 3770k are near as makes no difference identical, both 4core 8threaded chips, both clock reasonable well (IB limited due to poor TIM under IHS) (SB-E due to no unlocked multi)

Except the 3820 is rated for almost twice the power. I'd definitely choose the more energy-efficient revision over the old one any day.

As above, go with the 8350. They're not often recommended on this forum because many live by synthetic benchmarks. In highly-threaded, intensive, real-world apps (particularly video transcoding) the 8350 matches or beats the i7 3820. It's also better suited to VM's.

I went with AMD for my similar requirements. Although I also wanted to keep costs to a minimum so went with the FX-8 8320 and a 970 board. Including 16GB RAM and a new PSU the whole lot came to £300.
I can't speak for IvyBridge as I haven't used it but I'm happily running multiple server and desktop VMs with memory running out before CPU so I'll be upgrading to 32GB soon.

I went with AMD for my similar requirements. Although I also wanted to keep costs to a minimum so went with the FX-8 8320 and a 970 board. Including 16GB RAM and a new PSU the whole lot came to £300.
I can't speak for IvyBridge as I haven't used it but I'm happily running multiple server and desktop VMs with memory running out before CPU so I'll be upgrading to 32GB soon.

The trouble with them is they run too hot (so I dread to think what BD was like ), anyone claiming PD runs cool or has 4.6ghz+ overclock is either ignorant towards or just plain ignoring stress testing, Prime95 causes them to go beyond AMD recommended temps at only 4.2-4.4.